Wildcat Pictures
Background:
The wild cat is a wooden roller coaster named after of Hershey Park's very first coasters. It cost 5,000,000 dollars to build the coaster. The Wildcat has been in operation since May 26, 1996. This coaster was designed by Clair Hain and Mike Boodley, and was the first roller coaster built by Great Coasters International.
The Coaster:
There are twelve cars total
Two people per car
The sum of the masses of the carts is 5171 kg
Each cart is 1.09 meters long
Coaster is 13.1 meters in total length
Time--> 50.02s at top of the hill
Time-->119.68s or the total ride
Distance(y) vs Time
Acceleration(x) vs. Time
Acceleration(y) vs. Time
Acceleration(z) vs. Time Energy:
PE equals zero at 58 meters.
PE = KE
mgy = 0.5mv^2
gy = 0.5v^2
(9.8)(28.15)(2) = v^2t
23.5m/s
To begin conservation of energy was used to find the velocity of the coaster at the bottom of the first hill. PE was set to be zero at the bottom of the first hill so PE at the top of the hill was equal to KE at the bottom of the hill. The mass of the cart will cancel out leaving v^2 to equal 2gy. An altimeter was used to find y, this was found by subtracting the max height from the height at the bottom of the first hill (PE= 0). g is a constant. The calculated velocity was about 23.5m/s, however this did not take friction into account, so it was wrong.
The initial calculation of velocity was incorrect because it did not take friction into account. According to the Hershey Park website the maximum speed of the Wildcat is 21.5m/s. Using this as the velocity in the KE at the bottom of the first hill, the energy lost to friction as well as the coefficient of kinetic friction could be found. The total energy is the initial PE (mgy), this is equal to the KE at the bottom (0.5mv^2) plus the energy lost to friction along the way. The energy lost to friction is µN(d) where µ is the mean coefficient of kinetic friction on the first drop, N is the force the track applies on the coaster (this is equal to the force of gravity, mg, because of Newton's 3rd law), and d is the amount of track the coaster covers in the drop. Because the drop is in three dimensions (x,y,z) the value for d could no be found with the Distance(y) vs. Time, this made it pretty much impossible to get a 100% accurate value for d. d was calculated by finding the mean velocity of the ride (track length from Hershey Park website times our total time) and multiplying it by the time of the first drop (found with Distance(y) vs. Time graph). With a d value of 45.79, the mean coefficient of kinetic friction (µ) during the first drop was found to be 0.0997.
To find the force of the breaks it takes to stop the coaster at the end, the mass first has to be determined. The mass of the cart was listed on the Hershey Park's Website. The cart was 5,171 kg itself and then the mass of all the people in the coaster is added to it. There are twenty-four people in the coaster all at about 68.04 kg. The total mass for one cart in the Wildcat is 6,803.96 kg.
To determine the force of the breaks, the acceleration they cause was determined from the X-Acceleration vs. Time Graph in combination with the Distance(y) graph. The Distance(y) graph was used to find a time interval for the application of the breaks, the breaks were applied near the end and the ride was at a constant elevation.
F = ma
F = 6,804(-2.1)
F = -14,288N
The breaks are applied a total of three times. The first time brings the coaster almost to a complete stop, so the majority of the force is applied at that time.
Background:
The wild cat is a wooden roller coaster named after of Hershey Park's very first coasters. It cost 5,000,000 dollars to build the coaster. The Wildcat has been in operation since May 26, 1996. This coaster was designed by Clair Hain and Mike Boodley, and was the first roller coaster built by Great Coasters International.
The Coaster:
There are twelve cars total
Two people per car
The sum of the masses of the carts is 5171 kg
Each cart is 1.09 meters long
Coaster is 13.1 meters in total length
Time--> 50.02s at top of the hill
Time-->119.68s or the total ride
Distance(y) vs Time
Acceleration(x) vs. Time
Acceleration(y) vs. Time
Acceleration(z) vs. Time
Energy:
PE equals zero at 58 meters.
PE = KE
mgy = 0.5mv^2
gy = 0.5v^2
(9.8)(28.15)(2) = v^2t
23.5m/s
To begin conservation of energy was used to find the velocity of the coaster at the bottom of the first hill. PE was set to be zero at the bottom of the first hill so PE at the top of the hill was equal to KE at the bottom of the hill. The mass of the cart will cancel out leaving v^2 to equal 2gy. An altimeter was used to find y, this was found by subtracting the max height from the height at the bottom of the first hill (PE= 0). g is a constant. The calculated velocity was about 23.5m/s, however this did not take friction into account, so it was wrong.
PE = KE + µN(d)
mgy = 0.5mv^2 + µN(d)
mgy = 0.5mv^2 + µmg(d)
gy - 0.5v^2 = µg(d)
9.8(28.15) - 0.5(21.5)^2 = µ(9.8)(45.79)
µ = 0.0997
The initial calculation of velocity was incorrect because it did not take friction into account. According to the Hershey Park website the maximum speed of the Wildcat is 21.5m/s. Using this as the velocity in the KE at the bottom of the first hill, the energy lost to friction as well as the coefficient of kinetic friction could be found. The total energy is the initial PE (mgy), this is equal to the KE at the bottom (0.5mv^2) plus the energy lost to friction along the way. The energy lost to friction is µN(d) where µ is the mean coefficient of kinetic friction on the first drop, N is the force the track applies on the coaster (this is equal to the force of gravity, mg, because of Newton's 3rd law), and d is the amount of track the coaster covers in the drop. Because the drop is in three dimensions (x,y,z) the value for d could no be found with the Distance(y) vs. Time, this made it pretty much impossible to get a 100% accurate value for d. d was calculated by finding the mean velocity of the ride (track length from Hershey Park website times our total time) and multiplying it by the time of the first drop (found with Distance(y) vs. Time graph). With a d value of 45.79, the mean coefficient of kinetic friction (µ) during the first drop was found to be 0.0997.
To find the force of the breaks it takes to stop the coaster at the end, the mass first has to be determined. The mass of the cart was listed on the Hershey Park's Website. The cart was 5,171 kg itself and then the mass of all the people in the coaster is added to it. There are twenty-four people in the coaster all at about 68.04 kg. The total mass for one cart in the Wildcat is 6,803.96 kg.
To determine the force of the breaks, the acceleration they cause was determined from the X-Acceleration vs. Time Graph in combination with the Distance(y) graph. The Distance(y) graph was used to find a time interval for the application of the breaks, the breaks were applied near the end and the ride was at a constant elevation.
F = ma
F = 6,804(-2.1)
F = -14,288N
The breaks are applied a total of three times. The first time brings the coaster almost to a complete stop, so the majority of the force is applied at that time.